Solution of gauge theories induced by fundamental representation scalars
Abstract
Gauge theories induced by scalars in the fundamental representation of the U(Nc)gauge× U(Nf)global group are investigated in the large Nc and Nf limit. A master field is defined from bilinears of the scalar field following an Eguchi-Kawai type reduction of spacetime. The density function for the master field satisfies an integral equation that can be solved exactly in two dimensions (D=2) and in a convergent series of approximations at D>2. While at D=2 the system is in the same phase at all ε=Nc/Nf, it undergoes a phase transition at a critical value, εc(D), for D>2.
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